A Tensor-Product Finite Element Cochain Complex with Arbitrary Continuity

• Published in: arXiv.org
• Main Authors: Bonizzoni, Francesca, Kanschat, Guido
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 01.07.2022
• Subjects: Cartesian coordinates; Commutation; Computer Science - Numerical Analysis; Interpolation; Mathematical analysis; Mathematics - Numerical Analysis; Operators (mathematics); Smoothness; Tensors

We develop tensor product finite element cochain complexes of arbitrary smoothness on Cartesian meshes of arbitrary dimension. The first step is the construction of a one-dimensional \(C^m\)-conforming finite element cochain complex based on a modified Hermite interpolation operator, which is proved...